This paper aims at presenting the results from a research on the reasons why more than 50% of the small and medium size enterprises (SMEs) in European Union (EU) are non-innovative. The paper intends to find out which are the specific factors that influence the percentage of non-innovative industrial SMEs, considering that SMEs are the main stakeholders and target group of EU funds and policies, and industry is the main direction for economic development. The study employs a cross-sectional study and linear regressions. The findings after applying the research methodology show some already known factors that obstruct SMEs innovation performance like lack of internal finance and little market competition. However, the main contribution of the research is the finding that a low market demand does not contribute to an increase in the percentage of non-innovative enterprises. As a conclusion, all the measures and EU programs for boosting market demand for the purposes of increasing the number of innovative enterprises would be useless.